Graphical view of polynomial equations Problem set A Answers

1. (a) \(x = −2.30, 1.30, 2.00\)
2. (b) \(x = 2\); the graph touches the \(x\)-axis there and turns back

\(x = −3.32, −0.358, 1.68\)

\(y = (x + 6)^2 + 0\); vertex \((−6, 0)\); \(x = −6\)

1. (a) 1 different real root
2. (b) 2 different real roots
3. (c) 3 different real roots

\(t = 1.27, 3.00, 4.73\)

1. (a) \(a = 2\): 2; \(a = 3\): 3; \(a = 4\): 2
2. (b) A cubic goes from far below to far above the axis, so it must cross it. A quartic has both ends up, so it can sit above the axis.

1. (a) \(−16 < k < 16\)
2. (b) \(k = −16\) or \(k = 16\)

1. (a) \(k = 16\); \(x = 4\)
2. (b) 2 real roots